Solve the Quadratic Equation by Factorization: 4x² + 4bx − (a² − b²) = 0

Question: Solve the following quadratic equation by factorization:

$$ 4x^2+4bx-(a^2-b^2)=0 $$

Solution

$$ 4x^2+4bx+b^2-a^2=0 $$

$$ (2x+b)^2-a^2=0 $$

$$ (2x+b-a)(2x+b+a)=0 $$

Either

$$ 2x+b-a=0 $$

$$ x=\frac{a-b}{2} $$

or

$$ 2x+b+a=0 $$

$$ x=-\frac{a+b}{2} $$

Hence,

$$ \boxed{x=\frac{a-b}{2},\ -\frac{a+b}{2}} $$